This paper looks at axioms for convexity, and shows how they can be applied to discrete spaces. Two structures for a discrete geometry are considered: oriented matroids, and cell c...
We consider matroidal structures on convex geometries, which we call cg-matroids. The concept of a cg-matroid is closely related to but different from that of a supermatroid intro...
We relate the sequence of minimum bases of a matroid with linearly varying weights to three problems from combinatorial geometry: k-sets, lower envelopes of line segments, and con...
Let P be a set of n points in general position in the plane. Let Xk(P ) denote the number of empty convex k-gons determined by P. We derive, using elementary proof techniques, sev...
Pointed pseudo-triangulations are planar minimally rigid graphs embedded in the plane with pointed vertices (adjacent to an angle larger than π). In this paper we prove that the ...